Question: Find an explicit formula for the arithmetic sequence $81,54,27,0,...$. Note: the first term should be $\textit{a(1)}$. $a(n)=$
The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${81}$ and the common difference is ${-27}$. ${-27\,\curvearrowright}$ ${-27\,\curvearrowright}$ ${-27\,\curvearrowright}$ ${81},$ $54,$ $27,$ $0,...$ This is the explicit formula for the arithmetic sequence $81,54,27,0,...$. $a(n)={81}{-27}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.